(1) Field of the Invention
The present invention relates generally to a mechanical element having a pair of cooperative members, such as an outer member and a ball and such as an inner member and the ball of a uniform motion type universal joint constructed so as to relatively generate a harmonic vibration between the pair of members along with a sliding motion of one of the pair of members therebetween.
The present invention relates especially to the structure of the mechanical element described above in which a high frequency vibration is caused by the relative vibration due to a relative sliding motion between the pair of members.
(2) Description of the Background Art
FIG. 1 shows a cross sectional view of a conventional uniform motion type universal joint. The universal joint 1 shown in FIG. 1 serves to connect both rotational axles 2 and 3, respectively. The universal joint 1 serves to permit a transmission of an uniform velocity and a smooth rotary motion between the rotation axles 2 and 3, irrespective of a joint angle formed therebetween.
A structure of the uniform motion type universal joint will briefly be explained with reference to FIG. 1.
As shown in FIG. 1, a flange 2a is engaged with one end of one of the rotation axles 2. A ring shaped outer member 5 is coaxially fixed by means of a mounting bolt 4. An inner peripheral surface of the outer member 5 is formed with a plurality of ball rolling grooves 6 along its axial direction.
In addition, a ring shaped inner member 7 is axially engaged with one end of the other rotation axle 3 as shown in FIG. 1 so as to be enclosed with the outer member 5. An outer peripheral surface of the inner member 7 is formed so that the plurality of elongated ball running grooves 8 along the axial direction of the inner member 7 are opposed to the ball rolling groove 6 of the outer member 5.
Furthermore, a plurality of balls 10 are intervened between the outer member 5 and inner member 7 so as to be accommodated within the ball rolling grooves 6 and 8 and so as to be held by means of a ring shaped cage 9.
An action of a torque transmission between rotation axles 2 and 3 during a flexing of the uniform motion type universal joint 1 will be explained with reference to FIG. 2.
At first, suppose that one rotational axle 2 is a drive axle and the other rotational axle 3 is a driven axle.
Suppose that both rotational axle 2 and outer member 5 are rotated by a rotational speed .omega. input and the rotational force is transmitted toward the rotational axle 3 side via the uniform motion type universal joint 1 so that both inner member 7 and rotational axle 3 are rotated by a rotational speed .omega. output.
In addition, one of the balls 10 (hereinafter simply referred to as the ball) makes contact with the outer member 5 at a point a at an arbitrary time and makes contact with the inner wheel 7 at a point b also makes contact with the outer member 5 at a point a' and with the inner member 7 at a point b' after the uniform type universal joint 1 is further rotated through 90 degrees.
At this time, the ball 10 shown in FIG. 2 is always present at a position a distance R from a center axis of the outer member 5. A distance r.sub.1 from the center of the ball 10 to the contacts a, a' is constant. In addition, similarly, the ball 10 is always present at a position a distance R from the center axis of the inner member 7. A distance r.sub.2 from the center of the ball 10 to the contacts b, b' is constant as well.
Furthermore, suppose that an advance angle of the ball 10 after the uniform motion type universal joint 1 has been rotated by 90 degrees is .theta.' and the advance angle of the inner member 7 with respect to the ball 10 is .theta.". EQU .theta.=.theta.'+.theta." (1)
If the uniform motion type universal joint 1 has a function as, so called, the uniform motion type universal joint, the following formula should be established: EQU .omega. input=.omega. output (2)
If the equation (2) is satisfied and a uniform motion of the uniform motion type universal joint 1 is secured, EQU .theta.'=.theta." (3)
That is to say, the following equation represents a necessary and sufficient condition for an ideal uniform velocity and rotary motion: EQU .theta.'=.theta."=.theta./2 (4)
Suppose there is a relative motion relationship between the outer member 5 and the ball 10 and/or between the inner member 7 and ball 10 in the conventional uniform type universal joint 1.
That is to say, suppose during the 90 degree rotation of the uniform motion type universal joint 1, a rotational angle through which the ball 10 is rolled is .phi., a movement distance of the ball 10 (a distance between a-a') with respect to the outer member 5 is L.sub.1, a movement distance of the ball 10 (a distance between b-b') with respect to the inner member 7 is L.sub.2, and that the ball 10 is rolled on conditions that the ball 10 takes no smooth roll over both outer member 5 and inner member 7. If this supposition is correct, the following relationship should be established: EQU L.sub.1 =L.sub.2 ( 5)
From the above equation (5), the following equation (6) is also established: EQU r.sub.1 .multidot..phi.=r.sub.2 .multidot.(.phi.+.theta.) (6)
Therefore, the following equation (7) needs to be established: EQU (r.sub.2 -r.sub.1).multidot..phi.+r.sub.2 .multidot..theta.=0
The following equation (8) is a necessary condition if the equation (7) is always established for an arbitrary rotational angle .phi.. EQU r.sub.1 =r.sub.2, r.sub.2 =0 (8)
However, as a practical matter of fact, the equation (8) is not satisfied. Hence, there is an inconsistency in the above-described supposition, i.e., that the ball 10 shown in FIG. 2 is completely rolled over the outer member 5 and inner member 7 with no slide motion thereof.
This indicates that the ball 10 does not actually make a perfect rolling motion against the outer member 5 and inner member 7 but makes an imperfect rolling motion simultaneously with a slide motion.
As appreciated from the above, in the conventional uniform type universal joint 1, it is clear that the ball 10 makes not only a rolling motion against the outer member 5 and inner member 7 but also makes a slide motion against them and consequently, a vibration force due to the friction on a sliding portion of the respective members is imposed in a rotation axis direction.
How a vibration system to which the vibration force is applied responds to the input vibration force will be explained with reference to FIG. 6 which is a simple model showing a relationship of the torque transmission between the outer member 5 and ball 10 in the uniform motion type universal joint 1 (although the similar model is established between the inner member 7 and ball 10, it is omitted herein).
The following explanation refers to pages 1146 to 1152 of Japanese report "Japan Mechanics Society Volume C 49 No. 443".
FIG. 3 shows a vibration model of one degree of freedom representing the mechanical element shown in FIG. 1.
As shown in FIG. 3, suppose a one-degree of freedom vibration model has a mass M, a rigidity K of spring mass system, and an attenuation factor C. In addition, suppose a system in which a frictional force F which is dependent on a velocity dX/dt as shown in FIG. 7 is applied to the mass M of the system.
Suppose, furthermore, that a displacement vibration force Y is applied to the system; EQU Y=A.multidot.sin (.omega.t) (9)
It is noted that a reason that the displacement vibration force Y is a sinusodial wave is based on the fact that when, supposing the outer member 5 is fixed, the ball 10 takes one reciprocating motion within the ball rolling groove 6 of the outer member 5 during one rotation of the uniform type universal joint 1. That is to say, both outer member 5 and ball 10 constitute the mechanical element such that a relative harmonic vibration takes place along with the slide motion of the ball 10 on the outer member 5.
An equation of motion in the vibration system is expressed as follows: EQU M.multidot.d.sup.2 X/dt.sup.2 =-C (dX/dt-dY/dt)-K(X-Y)-F.multidot.sgn (dX/dt) (10)
In the equation (10), the following substitutions are carried out to be subjected to dimension-less equation:
K/M=.omega..sub.n.sup.2, PA1 C/M=2.xi..omega..sub.n, PA1 X/A=x, PA1 .omega./.omega..sub.n =.gamma., PA1 .omega..sub.n t=.gamma., and, PA1 F/KA=f. PA1 .xi.=0.1; and PA1 f=0.2; PA1 and the dimension-less input vibration frequency .gamma. is set as follows: .gamma.=0.2, that is to say, in a case where a rigidity in a vicinity to a portion at which the frictional force is generated is high.
Then, since EQU dx/dt=.omega..sub.n (dx/d.tau.) (11)
the equation (10) can be rearranged as follows: ##EQU1##
In this way, the dimension-less equation of motion can be derived which is determined by three parameters; an attenuation ratio .xi., a dimension-less input vibration frequency .gamma. which is a ratio between an input vibration frequency .omega. and an inherent natural frequency .omega. .sub.n, and a dimension-less frictional force f which is a ratio between a frictional force F and displacement input vibration force KA.
FIG. 8 shows a result of simulation for the equation of motion according to the equation (12) executed using a Runge-Kutta method.
As shown in FIG. 8, it is estimated that a dimension-less displacement x corresponding to a displacement of the mass M is affected by a high vibration frequency component which is not included in the input, i.e., displacement vibrating input since the frictional force F is present although the displacement input vibration force Y is sinusodial wave.
FIG. 9 shows a result of simulation executed in terms of frequency analysis in a case when the attenuation ratio .xi. and dimension-less frictional force f are fixed as follows:
As appreciated from a power spectrum shown in FIG. 9, it is confirmed that the vibration system shown in FIG. 3 generates high frequency vibrations (in the example shown in FIG. 3, the dimension-less frequencies over 0.6 as depicted in FIG. 9) which are different from the dimension-less input vibration frequency (in the example shown in FIG. 3, the dimension-less frequency of 0.2 as shown in FIG. 9).
As appreciated from the above observations, in the conventional uniform motion type universal joint 1, the ball 10 rolls and slides over the outer member 5 and inner member 7 and, therefore, high frequency vibrations due to the frictional force generated thereon provide a source of noise for a portion of such joints.
It is noted that such a problem as described above can be applied equally well to all systems represented by the model shown in FIG. 3, i.e., all mechanical elements having a pair of cooperative members which relatively and harmonically vibrate together due to the sliding motion therebetween.